The following line passes through point $(3, -6)$ : $y = \dfrac{2}{3} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(3, -6)$ into the equation gives: $-6 = \dfrac{2}{3} \cdot 3 + b$ $-6 = 2 + b$ $b = -6 - 2$ $b = -8$ Plugging in $-8$ for $b$, we get $y = \dfrac{2}{3} x - 8$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${11}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${\llap{-}11}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${11}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${\llap{-}11}$ $(3, -6)$